Power Factor Angle for Single Phase 3 Wire System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(2*Vac*I))
This formula uses 2 Functions, 4 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
Variables Used
Phase Difference - (Measured in Radian) - Phase Difference is defined as the difference between the phasor of apparent and real power (in degrees) or between voltage and current in an ac circuit.
Power Transmitted - (Measured in Watt) - Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work.
Voltage Underground AC - (Measured in Volt) - Voltage Underground AC is defined as the amount of work or force required to start the conduction of current within a line.
Current Underground AC - (Measured in Ampere) - Current Underground AC is defined as the current flowing through the overhead ac supply wire.
STEP 1: Convert Input(s) to Base Unit
Power Transmitted: 300 Watt --> 300 Watt No Conversion Required
Voltage Underground AC: 120 Volt --> 120 Volt No Conversion Required
Current Underground AC: 9 Ampere --> 9 Ampere No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Φ = acos(P/(2*Vac*I)) --> acos(300/(2*120*9))
Evaluating ... ...
Φ = 1.43145698603713
STEP 3: Convert Result to Output's Unit
1.43145698603713 Radian -->82.01644385446 Degree (Check conversion ​here)
FINAL ANSWER
82.01644385446 82.01644 Degree <-- Phase Difference
(Calculation completed in 00.004 seconds)

Credits

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Created by Urvi Rathod
Vishwakarma Government Engineering College (VGEC), Ahmedabad
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Chandigarh University (CU), Punjab
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Power and Power Factor Calculators

Transmitted Power using Volume of Conductor Material(1 Phase 3 Wire US)
​ LaTeX ​ Go Power Transmitted = sqrt(Line Losses*Volume Of Conductor*(Maximum Voltage Underground AC*cos(Phase Difference))^2/(10*Resistivity*(Length of Underground AC Wire)^2))
Power Factor using Volume of Conductor Material(1 Phase 3 Wire US)
​ LaTeX ​ Go Power Factor = sqrt(10*Resistivity*((Power Transmitted*Length of Underground AC Wire)^2)/(Line Losses*Volume Of Conductor*((Maximum Voltage Underground AC)^2)))
Power Factor using Load Current (1 Phase 3 Wire US)
​ LaTeX ​ Go Power Factor = sqrt(2)*Power Transmitted/(Maximum Voltage Underground AC*Current Underground AC)
Power Factor Angle for Single Phase 3 Wire System
​ LaTeX ​ Go Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))

Power Factor Angle for Single Phase 3 Wire System Formula

​LaTeX ​Go
Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC))
Φ = acos(P/(2*Vac*I))

What is the value of maximum voltage and volume of conductor material in 1-phase 3-wire system?

The volume of conductor material required in this system is 2.5/cos2θ times that of 2-wire d.c.system with the one conductor earthed. The maximum voltage between conductors is vm so that r.m.s. value of voltage between them is vm/√2.

How to Calculate Power Factor Angle for Single Phase 3 Wire System?

Power Factor Angle for Single Phase 3 Wire System calculator uses Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC)) to calculate the Phase Difference, Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power. Phase Difference is denoted by Φ symbol.

How to calculate Power Factor Angle for Single Phase 3 Wire System using this online calculator? To use this online calculator for Power Factor Angle for Single Phase 3 Wire System, enter Power Transmitted (P), Voltage Underground AC (Vac) & Current Underground AC (I) and hit the calculate button. Here is how the Power Factor Angle for Single Phase 3 Wire System calculation can be explained with given input values -> 4699.196 = acos(300/(2*120*9)).

FAQ

What is Power Factor Angle for Single Phase 3 Wire System?
Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power and is represented as Φ = acos(P/(2*Vac*I)) or Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC)). Power Transmitted is the amount of power that is transferred from its place of generation to a location where it is applied to perform useful work, Voltage Underground AC is defined as the amount of work or force required to start the conduction of current within a line & Current Underground AC is defined as the current flowing through the overhead ac supply wire.
How to calculate Power Factor Angle for Single Phase 3 Wire System?
Power factor angle for single phase 3 wire system formula is defined as the phase angle between reactive and active power is calculated using Phase Difference = acos(Power Transmitted/(2*Voltage Underground AC*Current Underground AC)). To calculate Power Factor Angle for Single Phase 3 Wire System, you need Power Transmitted (P), Voltage Underground AC (Vac) & Current Underground AC (I). With our tool, you need to enter the respective value for Power Transmitted, Voltage Underground AC & Current Underground AC and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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